Talks over a new contract for the German are believed to have been ongoing since October, with manager Pep Guardiola hopeful of a compromise being found.
City have been very active in tying down their stars to long-term deals of late, with Phil Foden, Raheem Sterling, Sergio Aguero, Kevin De Bruyne, Ederson, Gabriel Jesus, Nicolas Otamendi, David Silva and Fernandinho all putting pen to paper on fresh terms in the last year or so.
Sane joined City from Schalke back in the summer of 2016 and has quickly established himself as one of the Premier League's top attacking players and the 22-year-old says he would be more than happy to extend his stay with the club.
"From the beginning, when I arrived here, I have been really happy. I enjoy playing with the coach and the players," Sane enthused.
"They are all amazing but most importantly they are all amazing people and good characters.
"I have felt really at home here since day one and of course [signing an extension] is possible.
"Even if I am not playing for a certain time, I am still happy to be here and to play for this club, to work with these players and the coach.
"He is doing it good. Every one of us knows that we have to rotate sometimes because in every single position we have more than one or two good players.
"Obviously there is a time when you do not start from the beginning. You have to accept it. I think it is also good to put more pressure on everyone."